A New Optimization Model for the Sustainable Development: Quadratic Knapsack Problem with Conflict Graphs

Abstract

New information technology constantly improves the efficiency of social networks. Using optimization and decision models in the context of large data sets attracts extensive attention. This paper investigates a novel mathematical model for designing and optimizing environmental economic policies in a protection zone. The proposed model is referred to as the quadratic knapsack problem with conflict graphs, which is a new variant of the knapsack problem family. Due to the investigated problem processing a high complex structure, in order to solve efficiently the problem, we develop a metaheuristic which is based on the large neighborhood search. The proposed method embeds a construction procedure into a sophistical neighborhood search. For more details, the construction procedure takes charge of finding a starting solution while the investigated neighborhood search is used to generate and explore the solution space issuing from the provided starting solution. In order to highlight our theoretical model, we evaluate the model on a set of complex benchmark data sets. The obtained results demonstrate that the investigated algorithm is competitive and efficient compared to legacy algorithms.